Year 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 10 functions worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · FunctionsYear 10 Function Notation, Composites and Inverses Worksheet — Level 2 — Practice Set 4 — Answers
f(x) notation means "the value of the function at x". For a composite, substitute the inner function into the outer one. For an inverse, swap x and y and solve for y.
1.f(x) = −4x + 4 and g(x) = 5x − 3. Find f(g(x)) in simplest form.
Answer: −20x + 16
- f(g(x)) = −4(5x − 3) + 4
- = −20x + 16
2.f(x) = −2x − 5 and g(x) = 3x − 2. Find f(g(x)) in simplest form.
Answer: −6x − 1
- f(g(x)) = −2(3x − 2) − 5
- = −6x − 1
3.If f(x) = 2x2 + 5x + 6, find f(−4).
Answer: 18
- Replace x with −4: 2(−4)2 + 5(−4) + 6
- = 18
4.If f(x) = −3x2 − x, find f(1).
Answer: −4
- Replace x with 1: −3(1)2 − (1)
- = −4
5.If f(x) = −3x2 + 3x − 8, find f(3).
Answer: −26
- Replace x with 3: −3(3)2 + 3(3) − 8
- = −26
6.f(x) = x + 1 and g(x) = −x + 1. Find g(f(x)) in simplest form.
Answer: −x
- g(f(x)) = −1(x + 1) + 1
- = −x
7.If f(x) = −3x2 − 4x − 7, find f(4).
Answer: −71
- Replace x with 4: −3(4)2 − 4(4) − 7
- = −71
8.f(x) = −x − 6 and g(x) = −2x + 4. Find f(g(x)) in simplest form.
Answer: 2x − 10
- f(g(x)) = −1(−2x + 4) − 6
- = 2x − 10
9.f(x) = 3x − 5 and g(x) = 3x − 6. Find f(g(x)) in simplest form.
Answer: 9x − 23
- f(g(x)) = 3(3x − 6) − 5
- = 9x − 23
10.If f(x) = 4x2 + 5x + 5, find f(1).
Answer: 14
- Replace x with 1: 4(1)2 + 5(1) + 5
- = 14
11.If f(x) = −2x2 − 3, find f(5).
Answer: −53
- Replace x with 5: −2(5)2 − 3
- = −53
12.f(x) = −3x − 5 and g(x) = 4x − 4. Find g(f(x)) in simplest form.
Answer: −12x − 24
- g(f(x)) = 4(−3x − 5) − 4
- = −12x − 24
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